Construct the 5th term in sequence based on recursive definition. Show how you derive each term until the 5th. f(n)=2f(n-1)+n(n-1) f(1)=5

Q: Solve the inequality and graph the solution set. 4x + 2 6} K++++ -10-9-8-7-6-5-4-3-2-10 1 2 3 4 5 6…

A: The objective of the question is to solve the inequality 4x + 2 < 26 and find the correct…

Q: 15. In the following figure, two poles are 25 m and 15 m high. A cable 14 m long joins the tops of…

A: Pythagoras theorem is used

Q: Jane invest R8000 at an annual interest rate of 6% continuously compounded annually. how much will…

A: Here in this question we have to find how much will her investment be worth after 5 years. where the…

Q: Consider the following power series. Let an = I = 2 lim n→∞ an R = n+1 = Find the interval I and…

A:

Q: Suppose our recursive formula for a power series solution is a2 a3 Find the following in terms of ag…

A:

Q: Determine whether the series is absolutely convergent, conditionally convergent, or divergent.…

A: (.) given series is,                 (.) Absolutely convergent series: A series  is called…

Q: Use the divergence theorem to evaluate the surface integral JF CFN dS where F = 10xy²zi +10yrx²zj +…

A:

Q: 4. In the usual topology again, is locally compact? 5. Deduce. {(0, 0)} U {(x, y) = R²; x >0}

A: The given set is, .Locally compactness means that each point in the set has a compact neighborhood.

Q: Match the following series with the series below in which you can compare using the Limit Comparison…

A:

Q: -9 Using only a simple calculator, find the values of k such that det(M) = 0, where M = 1 your…

A:

Q: The figure shows level curves of a function f(x, y). (a) Draw gradient vectors at P and Q. Is Vf(P)…

A:

Q: Use the divergence theorem to evaluate the surface integral F. N dS where F = xy²i+yz²j + zx²k, S is…

A:

Q: Solving the IVP by the method of Laplace transform ý" – 5y +6y = u3(t) – u5(t), ý(0)=1, g(0)=0.

A:

Q: The graph of f(t) is given below. 765 4 7₁ 6 5 y 3₁ 2 1 t o 10 Find the Laplace transform F(s) =…

A: The given graph has 4 stages.       First stage:      for         Second stage:  The…

Q: 2. The behavior of the system is a saddle. x' = -x +y, y = -x-y

A: The given system of differential equations is:…

Q: 0.3 +0.03 +0.003 +0.0003 + ... (a) Express the series in the form M8 n=1 an (b) Does this series…

A: Series   0.3+0.03+0.003+0.0003+........general form of geometric progression terms is…

Q: 2 (90) 2 Determine if S={ all the correct answers }is a basis for R2 and check a. S is a basis b.s…

A: Note: '' As per guidelines we will solve first question. If you want any specific question to be…

Q: What is the longest line segment that can be drawn in a right rectangular prism that is 12 cm wide,…

A:

Q: The limit is equal to 0 ∞ -3 O 3 lim x→0 St³+27 dt X

A:

Q: Consider the topology 7 = {GCR:0 € Gor G=0} or T= on R. Is [0, 1) compact in (R, 7)? Explain why.

A: To determine whether the interval [0,1) is compact in the given topology τ on  we need to consider…

Q: (a) Sn (b) Sn = (c) Sn = (d) Sn 12n n+1 n+3.(-1)" 3n-1 (-2)" n-1 2nn²2n + 1 2 sin n n² + 2

A:

Q: Find the directions in the xy-plane in which the function f(x,y)=e¹-2xy has zero change at the point…

A: The given function is  and the point is .We have to find the direction in the plane in which the…

Q: 4. As a tornado moves, its speed increases. The function S(d) = 93 log d + 65 a) Graph this…

A: Given information:Function representing the speed of wind near the center of a tornado: , where  is…

Q: Write the system given system of differential equation in matrix form. Y₁' = 3y₁ + y2 + 3 sin(4x) Y2…

A: Given, system of differential equations,

Q: 1. Let f(z) = Z³ (z-i) Find Laurent Laurent series f(z) valid in the region A = { zec : 12-il > 1}

A: Given  The region is given by…

Q: (CONTROL SYSTEM) 1: Direction: solve for y(t) if all initial conditions are zero. Use Laplace…

A:

Q: A small country is comprised of four states, A, B, C, and D. The population of each state, in…

A:

Q: A company periodically produces a part that is a basic component of an assembled product. Each fixed…

A:

Q: 23. f(x) x + 1 at 1, (1, 2

A:

Q: 11/6 is the wrong answer

A:

Q: J cos(y + x) dA, Problem 6. Use a change of variables to evaluate where P is the parallelogram…

A:

Q: A bit string contains 1's and O's. How many different bit strings can be constructed given the…

A: There are a total of 10 positions in the first half of the string. To accommodate exactly 7 1's, we…

Q: Use de Moivre's Theorem to find the following. Write your answer in standard form. (√2 cis 77)

A:

Q: Use the limit comparison test to determine whether an = (a) Choose a series an lim n→∞ bn = lim n-x…

A:

Q: Approximately how much material is needed to make the tent illustrated in the following figure (both…

A: A graph of the tent is given, the aim is to find the amount of material needed to make the tent.

Q: Consider the equation 26 -1 = 0. (a) Find all the solutions to the above equation over C. (b) plot…

A:

Q: 4. Let S be a sphere of radius r and P a point inside or outside the sphere. Show that 1 √√₂₁ P |dx|…

A:

Q: payoff matrix for a game is given by -2] pute the expected payoffs of the game for the pairs of…

A: We will find the expected payoffs.

Q: Part II. Writing the equation d² dt2 in the form of the system dx d dt (c) (d) (e) = V, = x³ + x², X…

A: To solve part(d) , we need part(a),(b),(c) , that's why I am solving first four parts.

Q: a) Let p=13. Compute L2(3) b) Show that L2(11) = 7.

A: Here concept of field is used.

Q: please help show the step on how to get the correct asnwer. i have attached the correct answer…

A: Here the fircing function isu(t−2)={0t<21t≥2Given differential equationy″+y′+3y=u(t−2)The initial…

Q: a. The table below shows some input-output pairs for an exponential function f. x 0 1 2 3 f(x) 51.2…

A: An exponential function is a Mathematical function in the formf(x)=ax, where “x” is a variable and…

Q: (a) How many integers from 1 through 1,000 are multiples of 8 or multiples of 9? 164 X (b) Suppose…

A: The objective of the question is to find out the number of integers from 1 through 1000 that are…

Q: 1. Let S be the portion of the graph z=4 - 2x² - 3y² that lies over the region in the xy-plane…

A: \We have to set up the double integration

Q: Suppose R is the shaded region in the figure, and f(x, y) is a continuous function on R. Find the…

A:

Q: Find the following limit. √√x-4√√x 8%√x+4√√x lim 8118 lim 8118 5√x-4√x 8√x +4√x (Simplify your…

A:

Q: Evaluate 4+i 7/₂2 (46)^ 56 n=2 (b) > n=5 56

A:

Q: Find the unit tangent vector T and the principal unit normal vector N for the following…

A:

Q: Sketch the region of integration for O A. -9 Choose the correct sketch of the region below. 81- O B.…

A:

Q: Suppose T: R³ → R4 is a linear transformation with T(e₁) = T(es) = = A = 2 -14 H 5 8 NOTE: e; refers…

A:

Computational Systems

The computation systems can be defined as the systems that are capable of solving a problem that includes calculations either mathematical or logical, and are able to produce the result as an output. For example, a simple calculator that is given a set of numbers and operators as input and produces the result as an output can be defined as a computational system. The above example is a simple illustration only, the computational systems range from simple devices to complex devices such as the systems that control the SpaceX companies, Starlink satellites which are being quite recently seen in the skies at many places globally.